Question 992291: A car rental company offers two plans for renting a car.
Plan A: 38 dollars per day and 20 cents per mile.
Plan B: 57.04 dollars per day and 12 cents per mile.
If you plan to rent the car for one day, and m represents the number of miles driven in that day, for how many miles driven would you save money with plan B?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! equation for plan A is ca = 38 + .20 * x
equation for plan B is cb = 57.04 + .12 * x
question is for how many miles driven would you save money with plan B.
you will save money with plan B when the cost of plan B is less than the cost of plan A.
this means that cb < ca
replace cb with it's equation and replace ca with its equation to get:
57.04 + .12 * x < 38 + .20 * x
subtract 38 from both sides of this equation and subtract .12 * x from both sides of this equation to get:
57.04 - 38 < .20 * x - .12 * x
combine like terms to get:
19.04 < .08 * x
divide both sides of this equation by .08 to get:
19.04 / .08 < x
238 < x
solve for x to get x > 238 miles.
when x = 238 miles, plan A costs 85.6 and plan B costs 85.6.
plan B costs the same as plan A.
this is the break even point.
when x = 239 which is greater than 238, plan A costs 85.8 and plan B costs 85.72.
plan B is now cheaper than plan A and will remain cheaper as long as the number of miles driven is greater than 238.
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